The Parametric Complexity of Lossy Counter Machines (Track B: Automata, Logic, Semantics, and Theory of Programming)

Author Sylvain Schmitz

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Sylvain Schmitz
  • LSV, ENS Paris Saclay & CNRS, Université Paris-Saclay, France
  • IUF, France


I thank Philippe Schnoebelen for his comments on a preliminary draft.

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Sylvain Schmitz. The Parametric Complexity of Lossy Counter Machines (Track B: Automata, Logic, Semantics, and Theory of Programming). In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 129:1-129:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


The reachability problem in lossy counter machines is the best-known ACKERMANN-complete problem and has been used to establish most of the ACKERMANN-hardness statements in the literature. This hides however a complexity gap when the number of counters is fixed. We close this gap and prove F_d-completeness for machines with d counters, which provides the first known uncontrived problems complete for the fast-growing complexity classes at levels 3 < d < omega. We develop for this an approach through antichain factorisations of bad sequences and analysing the length of controlled antichains.

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational complexity and cryptography
  • Counter machine
  • well-structured system
  • well-quasi-order
  • antichain
  • fast-growing complexity


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